Related papers: K-Plane Regression
In this paper, we have considered general k-piece-wise linear convex loss functions in SVM model for measuring the empirical risk. The resulting k-Piece-wise Linear loss Support Vector Machine (k-PL-SVM) model is an adaptive SVM model which…
Existing works on "black-box" model interpretation use local-linear approximations to explain the predictions made for each data instance in terms of the importance assigned to the different features for arriving at the prediction. These…
We study the fundamental problem of fixed design {\em multidimensional segmented regression}: Given noisy samples from a function $f$, promised to be piecewise linear on an unknown set of $k$ rectangles, we want to recover $f$ up to a…
This paper introduces kernel continual learning, a simple but effective variant of continual learning that leverages the non-parametric nature of kernel methods to tackle catastrophic forgetting. We deploy an episodic memory unit that…
A fast and flexible $k$NN procedure is developed for dealing with a semiparametric functional regression model involving both partial-linear and single-index components. Rates of uniform consistency are presented. Simulated experiments…
A new approach for feature extraction from time series is proposed in this paper. This approach consists of a specific regression model incorporating a discrete hidden logistic process. The model parameters are estimated by the maximum…
A new statistical procedure, based on a modified spline basis, is proposed to identify the linear components in the panel data model with fixed effects. Under some mild assumptions, the proposed procedure is shown to consistently estimate…
This paper introduces the Partition Tree Weighting technique, an efficient meta-algorithm for piecewise stationary sources. The technique works by performing Bayesian model averaging over a large class of possible partitions of the data…
The complex nature of lithium-ion battery degradation has led to many machine learning based approaches to health forecasting being proposed in literature. However, machine learning can be computationally intensive. Linear approaches are…
Identifying breakpoints in piecewise regression is critical in enhancing the reliability and interpretability of data fitting. In this paper, we propose novel algorithms based on the greedy algorithm to accurately and efficiently identify…
This study introduces a general semiparametric clusterwise index distribution model to analyze how latent clusters affect the covariate-response relationships. By employing sufficient dimension reduction to account for the effects of…
This paper proposes a regularized pairwise difference approach for estimating the linear component coefficient in a partially linear model, with consistency and exact rates of convergence obtained in high dimensions under mild scaling…
How to develop slim and accurate deep neural networks has become crucial for real- world applications, especially for those employed in embedded systems. Though previous work along this research line has shown some promising results, most…
This paper is concerned with functional learning by utilizing two-stage sampled distribution regression. We study a multi-penalty regularization algorithm for distribution regression under the framework of learning theory. The algorithm…
In this paper, we propose a multi-kernel classifier learning algorithm to optimize a given nonlinear and nonsmoonth multivariate classifier performance measure. Moreover, to solve the problem of kernel function selection and kernel…
We propose a novel approach for change-point detection and parameter learning in multivariate non-stationary time series exhibiting oscillatory behaviour. We approximate the process through a piecewise function defined by a sum of…
(Neal and Hinton, 1998) recast maximum likelihood estimation of any given latent variable model as the minimization of a free energy functional $F$, and the EM algorithm as coordinate descent applied to $F$. Here, we explore alternative…
This paper presents a new algorithm for online linear regression whose efficiency guarantees satisfy the requirements of the KWIK (Knows What It Knows) framework. The algorithm improves on the complexity bounds of the current…
We present a new piecewise linear regression methodology that utilizes fitting a difference of convex functions (DC functions) to the data. These are functions $f$ that may be represented as the difference $\phi_1 - \phi_2$ for a choice of…
Linear regression is effective at identifying interpretable trends in a data set, but averages out potentially different effects on subgroups within data. We propose an iterative algorithm based on the randomized Kaczmarz (RK) method to…